1. Field of the Invention
The present invention relates to a method and an apparatus for the measurement of a void content and a particle content with the use of the X-ray small angle scattering method.
2. Description of the Related Art
The present invention relates to the measurement of the void content or the particle content of a sample made of a thin film which has a matrix and voids or particles dispersed in the matrix. The matrix represents the base material in which voids or particles exist. FIGS. 1A and 1B are exemplary sectional views of the sample to which the present invention is applied. The sample shown in Fig. IA is a thin film 10 on a substrate 18, the thin film 10 having a matrix 12 and voids 14 dispersed in the matrix 12. Thinking about the specific region of the thin film, a ratio of the total volume of the voids 14 existing in the region to the volume of the thin film in the region can be defined as a void content in the region. The sample shown in FIG. 1B is a thin film 10 having a matrix 12 and particles 16, whose material is different from the matrix, dispersed in the matrix 12. Similarly to the case having voids, thinking about the specific region of the thin film, a ratio of the total volume of the particles 16 existing in the region to the volume of the thin film in the region can be defined as a particle content in the region.
A technique of forming particles or voids with a nanometer size in a thin film gets a lot of attention in the recent development of the nanotechnology. The particles with a nanometer size are in the spotlight mainly in view of the improvement and variation of the properties caused by the quantum size effect. The voids with a nanometer size are expected to realize the porous interlayer insulation material in connection with the fine structure wiring of the semiconductor device. The particles or voids with a nanometer size can not be observed by the ordinary X-ray diffraction method because of the small periodicity. Therefore, the X-ray small angle scattering method and the EXAFS method would be important for observing the electron density fluctuation with a nanometer order. Especially, the X-ray small angle scattering method has been used from old times as the technique for evaluating the electron density fluctuation in a material with several nanometers to several hundred nanometers, for example, it has been used for the size evaluation of the particles or the voids and the evaluation of the long-period structure.
It is noted that the present invention relates to the measurement of the void content or the particle content of the sample with the use of the X-ray small angle scattering method, such a measurement is disclosed in Japanese patent publication No. 2001-349849 A, which will be referred to as the first publication. The first publication discloses the analysis of the thin film having voids or particles dispersed therein with the use of the X-ray small angle scattering method and the parameter fitting operation between the measured profile of the scattered intensity and the theoretical profile of the scattered intensity to determine the optimum values of the parameters. The embodiment of the first publication uses the scattering function for the theoretical profile of the scattered intensity, the function being a model in which the voids or the particles are assumed to be spherical or cylindrical and the size and its variance (which indicates the distribution of the size) are used as parameters to determine the size and the variance of the void or the particle. The first publication also discloses that a scattering function is produced using a void or particle content and its correlation distance as parameters, and a parameter fitting operation is carried out to determine the void or particle content and its correlation distance.
Formulae for determining the scattered X-ray intensity in connection with a thin film having voids or particles are disclosed in Japanese patent publication No. 2003-202305 A, which will be referred to as the second publication.
It is noted that the embodiment of the present invention carries out the measurement of the average density and the film thickness of the thin film using the X-ray reflectance method as the preliminary step before producing the theoretical profile of the X-ray small angle scattering, the measurement of the average density and the film thickness of the thin film using the X-ray reflectance method is known and disclosed in, for example, Japanese patent publication No. 10-38821 A (1998), which will referred to as the third publication.
Although the prior art disclosed in the first publication can measure the void or particle content using the X-ray small angle scattering method, the prior art has the problems described below. The method disclosed in the first publication uses a model in which the analysis is effective in the case that the proximal distance of the voids or particles is held at a certain distance, i.e., the state of the short-range-order. When the proximal distance of the voids or particles is held at a certain distance, a diffraction peak corresponding to the distance can be observed on the X-ray small angle scattering pattern. The proximal distance of the voids or particles and the void or particle content can be evaluated based on the appearance angle of the diffraction peak, which corresponds to the proximal distance, and the spread of the diffraction peak, which is evaluated with the full-width-at-half-maximum and corresponds to the void or particle content. This method is effective only in the case that the proximal distance is held at a certain distance and thus is not applicable to a system in which voids or particles are randomly dispersed.